Why doesn´t a guitar sound like a piano ?
by Perry Perreiter, Mediaproducer

This is the kind of question you may ask if you have ever played three chords on a guitar and hit three keys on a piano. And why do they - rightly in my opinion - claim the guitar to be the most flexible and colorful instrument in classical music?
In order to go into that matter I´ve arranged a mathematical model in my mind which is essentially based on the way of impact on the string. If and how this model is in harmony with physical reality I dare not judge. Anyway, you´ll be able to guess where we´re heading to ...

So what is it all about?
The most important difference between the two instruments is the way the string is made swing. While a guitar string is picked, the mechanics of a piano make a hammer hit the string. The essential thing is that picking a string happens in a punctiform way, while a hammer has a certain width and that´s why the string is stimulated along a certain length and not only in a single point.
Of course it also matters where the string is stimulated. If stimulated in the center, the sound of the string will appear more harmonical and smoother than stimulating it close to the ends of the string.

So how does a sound come into existance?
A sound is generated if many physical frequencies superpose. The so-called base frequency is responsible for the tone pitch we hear, while all the other frequencies determine the color of the sound. Now if a guitar and a piano play the same note, let it be an A with f0=442 Hz, both sounds have the same base frequency (442 Hz), but there are harmonics of completely different kind and composition. Harmonics may be interpreted as multiples in whole numbers of the base frequency.

The sound of the center
If a string (no matter if guitar or piano) is stimulated at the center, there are only odd multiples of the base frequency. As the frequencies 2*f0, 4*f0, ... are missing, there are no octaves. Instead, the first harmonic is a quint (3*f0). This quint and the lacking of the octave lead to a harmonical sound experience.

The sound of the guitar
Picking a string in a punctiform way makes the harmonies emerge very quietly compared to the base frequency. In picking, the more you move away from the center, the louder the harmonics get, and it´s especially the octaves that rise along with the odd multiples of the base frequency, the sound gets less pure.

The sound of the hammer
Hitting a string with a hammer also produces harmonics, but these are much louder than picking a string. The base frequency is clearly overlaid by the first octave, which does not lead to a self-resting sound but rather to an entanglement of frequencies typical for a piano for instance.

Visualization
Take a look at this idealized, extremely slowed down and exaggerated presentation:

Swinging String

The sound of the guitar - revisited
Watching the complex swinging of the string, you may fancy what is going to happen if you relieve the string of its mathematical model and put it into physical reality, where a string is not frictionless, without mass and infinitely strechy, and where temperature, humidity, air pressure, material, the virtuosity of the guitarist and last but not least the secrets of the luthier and the guitar itself play a major role.



http://www.perreiter.de

March 22, 2005